A few years ago, I started trying out some new formative assessment techniques. It has been a journey full of surprises. I’ve learned a lot about what my students think along the way. One of the big surprises was during a unit introducing ratios. I gave my students this exit ticket.

When I made it, I was just trying out the structure and thought it was a little bit of fluff. Then, I saw the results. I gave the assessment about a week into a unit introducing ratio reasoning to my sixth grade class. We had completed lessons on tape diagrams, ratio tables, and double number lines. I expected students to just plop those three representations into the exit ticket without much thought. Instead, I got 3:2, 3 to 2, and 3/2.

I’ve given a lot of thought to why I got these responses. Did the students just key in on the “3” part of the question and not really read the prompt carefully? Did I fail to draw out the connections between tape diagrams, ratio tables, and double number lines enough? I don’t know why I got the responses that I did, but pondering the question of why was important. I started working harder at drawing out the connections between the different representations the next year and the next.

I gave this assessment a few days ago. As I walked around the room, I marked each response with either a green or a pink highlighter. Most of the responses were correct. Those students who got a pink mark, went back through their interactive notebook to find their mistakes and correct them.

I still wonder why some of my students are making this mistake, but feel a little closer to the answer.

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I like this method of assessment. Going to try to see how I might use in Int. Math 2. What’s a double number line?

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A double number line is a model used to show equivalent ratios. One item being compared is shown on the top number line and the other item is shown on a number line below it. The number lines are structured so that anywhere you cut them, you will see an equivalent ratio. Double number lines and tape diagrams are part of the modeling component of the Common Core State Standards for ratios in 6th grade.

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